⠀⠀⠀⠀⣴⡟⠳⣆⠀⠀⠀⠀⠀⠀⢠⡾⠛⣶⡀⠀⠀⠀
⠀⠀⠀⢸⡿⠀⠀⠙⣿⢹⣿⢻⡇⡾⠟⠁⠀⠈⢿⡀⠀⠀
⣤⣄⣄⠿⠁⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⢀⠷⠶⠶
⣀⣤⡤⡄⠀⠾⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠆⠲⢦⣤
⠉⠀⠀⢿⣌⣛⣥⣤⣄⡳⠞⠲⢟⣤⣤⣴⣿⣃⣸⠇⠀⠀
⠀⠀⠀⢠⠞⠛⢻⡀⠀⠙⢦⣀⡾⠋⢹⠟⠛⠻⣶⠀⠀⠀
⠀⠀⠀⠙⣆⣀⣀⡼⠀⠀⠀⠈⠀⠀⠀⠙⢦⣀⣤⠇⠀⠀
⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢷⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡏⠳⣤⡀⠀⠀⠀⠀⢀⡴⠋⠁⢹⣧⠤⢶
⠀⠀⠀⠀⠀⠀⣿⠀⣶⠿⠷⢦⣀⠼⠿⢶⠄⠀⣼⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠙⠷⠛⠀⠀⠀⠈⠀⠀⠀⠛⠾⠋⠀⠀⠀

⠀⠀⠀⠀⣴⡟⠳⣆⠀⠀⠀⠀⠀⠀⢠⡾⠛⣶⡀⠀⠀⠀
⠀⠀⠀⢸⡿⠀⠀⠙⣿⢹⣿⢻⡇⡾⠟⠁⠀⠈⢿⡀⠀⠀
⣤⣄⣄⠿⠁⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⢀⠷⠶⠶
⣀⣤⡤⡄⠀⠾⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠆⠲⢦⣤
⠉⠀⠀⢿⣌⣛⣥⣤⣄⡳⠞⠲⢟⣤⣤⣴⣿⣃⣸⠇⠀⠀
⠀⠀⠀⢠⠞⠛⢻⡀⠀⠙⢦⣀⡾⠋⢹⠟⠛⠻⣶⠀⠀⠀
⠀⠀⠀⠙⣆⣀⣀⡼⠀⠀⠀⠈⠀⠀⠀⠙⢦⣀⣤⠇⠀⠀
⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢷⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡏⠳⣤⡀⠀⠀⠀⠀⢀⡴⠋⠁⢹⣧⠤⢶
⠀⠀⠀⠀⠀⠀⣿⠀⣶⠿⠷⢦⣀⠼⠿⢶⠄⠀⣼⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠙⠷⠛⠀⠀⠀⠈⠀⠀⠀⠛⠾⠋⠀⠀⠀

⠀⠀⠀⠀⣴⡟⠳⣆⠀⠀⠀⠀⠀⠀⢠⡾⠛⣶⡀⠀⠀⠀
⠀⠀⠀⢸⡿⠀⠀⠙⣿⢹⣿⢻⡇⡾⠟⠁⠀⠈⢿⡀⠀⠀
⣤⣄⣄⠿⠁⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⢀⠷⠶⠶
⣀⣤⡤⡄⠀⠾⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠆⠲⢦⣤
⠉⠀⠀⢿⣌⣛⣥⣤⣄⡳⠞⠲⢟⣤⣤⣴⣿⣃⣸⠇⠀⠀
⠀⠀⠀⢠⠞⠛⢻⡀⠀⠙⢦⣀⡾⠋⢹⠟⠛⠻⣶⠀⠀⠀
⠀⠀⠀⠙⣆⣀⣀⡼⠀⠀⠀⠈⠀⠀⠀⠙⢦⣀⣤⠇⠀⠀
⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢷⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡏⠳⣤⡀⠀⠀⠀⠀⢀⡴⠋⠁⢹⣧⠤⢶
⠀⠀⠀⠀⠀⠀⣿⠀⣶⠿⠷⢦⣀⠼⠿⢶⠄⠀⣼⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠙⠷⠛⠀⠀⠀⠈⠀⠀⠀⠛⠾⠋⠀⠀⠀

⠀⠀⠀⠀⣴⡟⠳⣆⠀⠀⠀⠀⠀⠀⢠⡾⠛⣶⡀⠀⠀⠀
⠀⠀⠀⢸⡿⠀⠀⠙⣿⢹⣿⢻⡇⡾⠟⠁⠀⠈⢿⡀⠀⠀
⣤⣄⣄⠿⠁⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⢀⠷⠶⠶
⣀⣤⡤⡄⠀⠾⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠆⠲⢦⣤
⠉⠀⠀⢿⣌⣛⣥⣤⣄⡳⠞⠲⢟⣤⣤⣴⣿⣃⣸⠇⠀⠀
⠀⠀⠀⢠⠞⠛⢻⡀⠀⠙⢦⣀⡾⠋⢹⠟⠛⠻⣶⠀⠀⠀
⠀⠀⠀⠙⣆⣀⣀⡼⠀⠀⠀⠈⠀⠀⠀⠙⢦⣀⣤⠇⠀⠀
⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢷⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡏⠳⣤⡀⠀⠀⠀⠀⢀⡴⠋⠁⢹⣧⠤⢶
⠀⠀⠀⠀⠀⠀⣿⠀⣶⠿⠷⢦⣀⠼⠿⢶⠄⠀⣼⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠙⠷⠛⠀⠀⠀⠈⠀⠀⠀⠛⠾⠋⠀⠀⠀

⠀⠀⠀⠀⣴⡟⠳⣆⠀⠀⠀⠀⠀⠀⢠⡾⠛⣶⡀⠀⠀⠀
⠀⠀⠀⢸⡿⠀⠀⠙⣿⢹⣿⢻⡇⡾⠟⠁⠀⠈⢿⡀⠀⠀
⣤⣄⣄⠿⠁⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⢀⠷⠶⠶
⣀⣤⡤⡄⠀⠾⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠆⠲⢦⣤
⠉⠀⠀⢿⣌⣛⣥⣤⣄⡳⠞⠲⢟⣤⣤⣴⣿⣃⣸⠇⠀⠀
⠀⠀⠀⢠⠞⠛⢻⡀⠀⠙⢦⣀⡾⠋⢹⠟⠛⠻⣶⠀⠀⠀
⠀⠀⠀⠙⣆⣀⣀⡼⠀⠀⠀⠈⠀⠀⠀⠙⢦⣀⣤⠇⠀⠀
⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢷⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡏⠳⣤⡀⠀⠀⠀⠀⢀⡴⠋⠁⢹⣧⠤⢶
⠀⠀⠀⠀⠀⠀⣿⠀⣶⠿⠷⢦⣀⠼⠿⢶⠄⠀⣼⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠙⠷⠛⠀⠀⠀⠈⠀⠀⠀⠛⠾⠋⠀⠀⠀

⠀⠀⠀⠀⣴⡟⠳⣆⠀⠀⠀⠀⠀⠀⢠⡾⠛⣶⡀⠀⠀⠀
⠀⠀⠀⢸⡿⠀⠀⠙⣿⢹⣿⢻⡇⡾⠟⠁⠀⠈⢿⡀⠀⠀
⣤⣄⣄⠿⠁⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⢀⠷⠶⠶
⣀⣤⡤⡄⠀⠾⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠆⠲⢦⣤
⠉⠀⠀⢿⣌⣛⣥⣤⣄⡳⠞⠲⢟⣤⣤⣴⣿⣃⣸⠇⠀⠀
⠀⠀⠀⢠⠞⠛⢻⡀⠀⠙⢦⣀⡾⠋⢹⠟⠛⠻⣶⠀⠀⠀
⠀⠀⠀⠙⣆⣀⣀⡼⠀⠀⠀⠈⠀⠀⠀⠙⢦⣀⣤⠇⠀⠀
⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢷⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡏⠳⣤⡀⠀⠀⠀⠀⢀⡴⠋⠁⢹⣧⠤⢶
⠀⠀⠀⠀⠀⠀⣿⠀⣶⠿⠷⢦⣀⠼⠿⢶⠄⠀⣼⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠙⠷⠛⠀⠀⠀⠈⠀⠀⠀⠛⠾⠋⠀⠀⠀